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  "body": "\n## Summary\n\nThe Minkowski–Bouligand dimension is also called the box-counting dimension.\nFor a bounded set, it measures how fast the number of small boxes needed to cover the set grows as the boxes shrink.\nIf about $\\varepsilon^{-d}$ boxes of side $\\varepsilon$ are needed, the dimension is $d$.\nIt is easy to estimate numerically, and it is at least the [[Hausdorff dimension|SSNFTHZ6YJ]].\n\n## Explanations\n\n### L1 human\n\nLay a grid of squares of side $\\varepsilon$ over a picture of the set and count the squares that meet it.\nFor a segment, halving $\\varepsilon$ doubles the count; for a filled square, it multiplies the count by four.\nThe exponent in this growth is the box-counting dimension: $1$ for the segment and $2$ for the square.\nFor the middle-thirds Cantor set, dividing $\\varepsilon$ by $3$ doubles the count, which gives dimension $\\log 2 / \\log 3$.\n",
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